LEC method for growing a single crystal of compound semiconductors

ABSTRACT

If the distribution coefficient of an impurity in a compound melt is less than 1, the impurity concentration in the compound melt doped with the impurity increased during a crystal growth in an LEC method. A supplying device replenishes an undoped crystal into the melt in order to keep the impurity concentration constant. The undoped crystal is covered with a liquid encapsulant which is contained in an encapsulant-supporting-cylinder or double-cylinder. Replenishing rate (dQ/dt) of the undoped crystal and the growing rate (dS/dt) should satisfy the equation 
     
         dQ/dt=(1-k)dS/dt 
    
     The impurity concentration of a grown single crystal is uniform. Whole of the crystal is a single crystal. Electronic properties of the single crystal is uniform from seed end to tail end.

BACKGROUND OF THE INVENTION

This invention relates to an improvement of a liquid encapsulatedCzockralski method (LEC method) for growing a single crystal of compoundsemiconductors.

In growing a single crystal of compound semiconductors, various kinds ofelements are usually doped in order to change electronic characteristicsor to reduce the dislocation density of the single crystal.

For example, some elements which have a different valence number fromthat of matrix elements of the semiconductor crystal are doped asimpurity in order to make the grown crystal into an n-type semiconductoror a p-type semiconductor.

In this invention compound semiconductors mean semiconductors of groupsIII-V and groups II-VI in the periodic table.

For example GaAs, GaP, InP, GaSb, etc are semiconductors of groupsIII-V. CdS, CdSe, CdTe, etc are semiconductors of groups II-VI.

For example in the case of growing a single crystal of GaAs,isoelectronic impurities--B, In, Sb, etc--are doped in order to reducethe dislocation density in the single crystal. Isoelectronic impurity isdefined as an impurity whose valence number is the same with one of thematrix elements of semiconductor crystals.

Besides, S, Te, Si, etc which are not isoelectronic impurities are dopedinto GaAs single crystals to change electronic characteristics.

A liquid encapsulated Czockralski method (LEC method) is one of theprevailing methods used to grow a single crystal of semiconductor.

An LEC method comprises: melting encapsulant material and compoundmaterial into a compound melt covered with a liquid encapsulant in acrucible by heating, dipping a seed crystal into the compound melt,growing a single crystal from the compound melt by pulling up androtating the seed crystal and cooling the grown crystal in a coolingzone above the crucible.

In the case of doping some impurities, the impurities ae added into thecompound material as elements or compound which comprise the impurityelements.

When a single crystal is grown from a compound melt which includes animpurity element, the impurity concentration C_(s) in a solidifiedsingle crystal pulled up is not equal to the impurity concentrationC_(L) in the compound melt in general.

The boundary between a compound melt and a solidified single crystal iscalled a liquid-solid interface. Generally the ratio of the impurityconcentrations of a solidified part to that of a melt is a constantvalue, which is called a distribution coefficient.

The distribution coefficient depends upon a pressure acting on the meltand a ratio of elements of matrix compound in the melt. But if thepressure is kept constant, the distribution coefficient is constant inthe crystal growth.

The distribution coefficient k is defined by

    k=C.sub.s /C.sub.L                                         ( 1)

If the impurity concentration is 1 in a melt, the impurity concentrationof the solidified part at the liquid-solid interface is k.

Distribution coefficients are defined by determining an impurity elementand a matrix melt. They obtain various values according to the impurityelement and the matrix melt. When the impurity element and the matrixmelt are identified, the distribution coefficient changes as a functionof pressure.

But in many cases the distribution coefficient is smaller than 1. If theimpurity has a distribution coefficient smaller than 1, impurity atomsdo not easily penetrate into the solidified part. When a single crystalis pulled up from a compound melt including an impurity element by anLEC method, the compound elements of the matrix of the crystal areremoved from the crucible more rapidly than the impurity element. Thenthe impurity concentration in the melt gradually increases during thecrystal growth.

The impurity concentration C in a crystal grown by an LEC method isgiven by

    C=C.sub.0 k(1-g).sup.k-1                                   ( 2)

Where C₀ is an initial impurity concentration in the compound melt and gis a ratio of solidified part to the initial compound melt by weight.This ratio is called solidification ratio from now for simplicity.

At the initial state the solidification ratio g is zero. During thecrystal growth the solidification rate g increases.

If the distribution coefficient k is smaller than 1, the impurityconcentration C is lowest at the beginning of the crystal growth,because the solidification rate g is zero. And the impurityconcentration C raises as the crystal growth proceeds. When thesolidification rate g comes near to 1, the impurity concentrationdiverges.

Accordingly if the impurity having a distribution coefficient k lessthan 1 is doped in a compound melt, the impurity concentration C islowest at a seed end of a single crystal grown from the melt and ishighest at a tail end of the crystal.

A single crystal ingot grown by the LEC method is sliced in the planeswhich are perpendicular to the growth axis. Sliced crystals are calledwafers. According to the explanation abovementioned, the impurityconcentration is different with regard to each wafer sliced from thesame crystal ingot. Therefore it is difficult to make many wafers havingthe same characteristics by the LEC method.

Furthermore when the impurity concentration in the initial melt is veryhigh, the impurity concentration in the melt raises higher than a limitof single-crystallization. Separating of impurity atoms on the surfaceof the pulled crystal happens. After the separating occurs, thesolidified part does not become a single crystal. Therefore, only asmall upper portion of the ingot is available, because a semiconductorwafer must be a single crystal.

It is desirable that the grown ingot should be a single crystal fromseed end to tail end and the impurity concentration should be uniform inthe single crystal.

If a great amount of compound melt which is many times larger than thecrystal to be grown are contained in a big crucible, the change of theimpurity concentration during the crystal growth might be trivial.

But in the practical case the diameter of a crucible is determined to betwice as big as the diameter of the single crystal grown from thecrucible, and the depth of the crucible is nearly equal to the diameterof the crystal. Thus it is impossible to use excessively much compoundmelt.

SUMMARY OF THE INVENTION

An object of the invention is to provide an LEC method and apparatus forgrowing a single crystal of compound semiconductors wherein the whole ofthe grown crystal is single and the impurity concentration is uniformfrom seed end to tail end of the single crystal.

The LEC apparatus of this invention has a device for supplying compoundmaterial into the melt to keep the impurity concentration constant inthe melt during the crystal growth. The supplying device holds anundoped polycrystal or single crystal of compound material and dipslittle by little the compound material into the melt. The replenishedmaterial compensates for the decrease of the material removed by thegrown crystal.

Mathematical consideration will clarify the features of the invention.

"L" denotes a weight of compound melt. "S" denotes a weight of thesingle crystal grown from the compound melt. "Q" denotes a weight of apolycrystal or single crystal replenished into the melt by the supplyingdevice. And "m" denotes a weight of an impurity in the compound melt.

The following equations hold. When the single crystal is pulled more byan infinitesimal weight dS and the impurity in the compound meltdecreases by an infinitesimal weight (-dm), the decrement (-dm) is givenby

    -dm=kCdS                                                   (3)

because CdS is the weight of impurity included in the infinitesimal partdS of the melt and kCdS is the weight of impurity included in theinfinitesimal part dS of the crystal pulled from the melt.

The sum of the increment of the weight of the crystal and the incrementof the weight of the melt must be zero, if the compound material is notreplenished like conventional LEC methods. However, the apparatus of theinvention replenishes compound material into the melt. Then the sum ofthe increments of the weights of the melt and the crystal must be thereplenished amount of the compound material. Thus we obtain

    dS+dL=dQ                                                   (4)

The impurity weight m in the melt must be equal to the product of themelt weight L and the impurity concentration C in the melt. Hence,

    CL=m                                                       (5)

Eq.(3), Eq.(4), and Eq. (5) are fundamental equations.

If we assume the impurity concentration C should be constant during acrystal growth, the infinitesimal increment dC is zero. Bydifferentiating Eq.(5) and substituting Eq.(3) and Eq.(4) into thedifferential equation, we obtain

    dQ=(1-k)dS                                                 (6)

    dL=-kdS                                                    (7)

    dm=-kCdS                                                   (8)

Eq.(6) is an important equation for this invention. From Eq.(6) when thecrystal is pulled more by dS, the replenishment of polycrystal or singlecrystal by (1-k) dS will keep the impurity concentration constant.

In the case of the compound semiconductor of group III-V, the elementsof group V are apt to escape from the polycrystal or single crystal tobe replenished in the melt. To prevent this phenomenon, a liquidencapsulation should be required.

The liquid encapsulant should be B₂ O₃ in the case of the crystal growthof GaAs. The density of the B₂ O₃ is considerably smaller than that ofGaAs. Then the liquid encapsulant B₂ O₃ can cover a polycrystal orsingle crystal of GaAs up to a definite level much higher than theliquid-solid interface in the crucible.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a sectional view of an LEC apparatus for growing a singlecrystal of compound semiconductors according to a first embodiment ofthe invention.

FIG. 2 is a sectional view of an LEC apparatus for growing a singlecrystal of compound semiconductors according to a second embodiment ofthe invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In FIG. 1 a heater (1) is a cylindrical resistance heater. A lower shaft(2) is a vertical shaft which can rotate and move upward or downward. Asusceptor (3) is supported at the top end of the lower shaft (2). Acrucible (4) is inserted into the susceptor (3). The crucible (4) ismade from quartz, PBN (pyrolytic boron nitride), etc.

There is a compound melt (5) in the crucible (4). The compound melt (5)keeps a liquid state, because it is heated by the heater (1). Thecompound melt (5) consists of pure material of matrix compound and someimpurities.

A liquid encapsulant (6) covers on the upper surface of the compoundmelt (5). The liquid encapsulant (6) prevents an element of group V witha high dissolution pressure from escaping out of the crystal.

If the compound melt is GaAs, a most preferable liquid encapsulant is B₂O₃. If the compound melt is GaSb, a most preferable liquid encapsulantis an eutectic of KCl and NaCl.

These members are contained in a pressurized chamber in which nitrogengas or inert gas (Ar, He, etc) is filled at a high pressure. Thepressurized chamber is not shown in the figures for simplicity.

From an upper region of the pressurized chamber an upper shaft (13) isretained along a vertical line.

A seed crystal (7) is fixed to the bottom end of the upper shaft (13).The upper shaft (13) can rotate and move upward or downward arbitrarily.

By dipping the seed crystal (7) into the compound melt (5) and pullingup the seed crystal (7) with a certain rotation speed, a single crystal(8) is pulling up, succeeding to the seed crystal (7).

The structure mentioned so far is the same with that of the conventionalLEC apparatus.

Besides these members the LEC apparatus of this invention has a devicefor supplying compound material little by little into the melt (5) tokeep the impurity concentration constant. This is an importantcharacteristic of the invention.

The compound material to be replenished is either an undoped polycrystalor single crystal of the compound semiconductor to be grown. Then thematerial to be replenished is called an "undoped crystal" in common.

In the embodiment shown in FIG. 1 an undoped crystal (9) is formed in along, round stick. The upper end of the undoped crystal (9) is supportedby a supplying shaft (10) which can rotate and move upward or downward.

Bottom end (17) of the undoped crystal (9) contacts with the compoundmelt (5) and is melted little by little by the heat transmitted from themelt (5). Molten material dissolves in and mixes with the melt (5).

Because compound material is replenished into the melt (5), the impurityis diluted by the newly-replenished material of matrix compound. Todilute the impurity uniformly, the crucible (4) and the single crystal(8) are rotated. The rotational motion helps the impurity mix with thematrix material.

By controlling the speed of dipping of the undoped crystal (9) into themelt (5), we can suppress the increase of the impurity concentration,keep the impurity concentration constant or reduce it also.

The undoped crystal must be covered by a pertinent liquid encapsulant toprevent the element of group V from escaping out of the undoped crystal.A cylinder (12) is suspended from a sustaining device (not shown in thefigures) above the crucible. The cylinder (12) encloses the undopedcrystal (9). Between the pillared undoped crystal (9) and the innersurface of the cylinder (12) a liquid encapsulant (16) is filled.

The liquid encapsulant (16) covers greater part of the undoped crystal(9) from the bottom end. Thus the cylinder (12) is called anencapsulant-supporting cylinder.

The element of group V is apt to escape from the compound crystal ofgroups III-V only when the crystal is heated up to a high temperature.The pillared undoped crystal (9) is hottest at the bottom end. Thus theliquid encapsulant (16) must cover the lower half of the pillaredundoped crystal (9).

In the case of the crystal growth of GaAs, the liquid encapsulant (16)is B₂ O₃. B₂ O₃ is solid at a room temperature. B₂ O₃ is melted intoliquid by heating it at about 500° C. to 600° C. Fortunately at 500° C.to 600° C. As dose not escape from a GaAs crystal.

Then a local heater (14) is installed n the middle region of theencapsulant-supporting-cylinder (12) in order to heat the upper portionof the liquid encapsulant (16). The heater (14) melts the encapsulantmaterial into a liquid state. Whole encapsulant material keeps a liquidstate by the heat generated at the main heater (1) and the local heater(14). Thus the local heater (14) is called an encapsulant-heater.

Because the encapsulant is liquid throughout the full length, andbecause the upper surface of the liquid encapsulant is pressurized bynitrogen gas at a high pressure, the liquid encapsulant effectivelyprevents As from escaping out of the strongly-heated bottom region ofthe undoped GaAs crystal.

The speed for supplying the undoped crystal (9) into the compound melt(5) determines the variation of the impurity concentration in thecompound melt (5).

In order to keep the impurity concentration constant, the supplyingspeed of the undoped crystal is given by

    dQ/dt=(1-k)dS/dt                                           (9)

according to Eq.(6). Here dQ/dt means the supplying speed. It is aweight of undoped crystal which is supplied into the melt in a unittime. dS/dt means a speed of the crystal growth. It is a weightincrement of the growing crystal in a unit time.

Now more specialized case is considered to use more measurableparameters. We assume the single crystal (8) has a round section with aradius E and the undoped crystal (9) has a round section with a radiusF. "U*" denotes a relative line velocity for pulling the single crystal(8) with regard to a liquid-solid interface (15). "V*" denotes arelative line velocity for dipping the undoped crystal (9) with regardto a liquid-solid interface (17). The ascending velocity U* and thedescending velocity V* must satisfy the equation

    F.sup.2 V*=(1-k)E.sup.2 U*                                 (10)

in order to keep the impurity concentration constant.

Strictly speaking the liquid-solid interfaces (15) and (17) move upwardor downward by vertical displacements of the lower shaft (2) and theupper shaft (13). "W" is an ascending velocity of the lower shaft.Because W is the ascending velocity, W is negative when the lower shaftis descending. "U" is an ascending velocity of the upper shaft (13).This is not a relative velocity but an absolute velocity. U is notidentical to U* in Eq.(10). "V" is a descending velocity of thesupporting shaft (10). This is not a relative velocity. V is notidentical to V* in Eq.(10). "A" is an area of the liquid-solid interface(15). "B" is a sectional area of the single crystal (8). "C" is asectional area of the undoped crystal (9) to be replenished.

The condition for keeping the impurity concentration constant in thecompound melt (5) is given by ##EQU1##

When Eq.(9) is not rigorously satisfied, the impurity concentration willvary. The rate of variation is calculated from

    dC/CL=(1-k)dS-dQ                                           (12)

In Eq.(12) dS and dQ are independent variables. From Eq.(12) when themelt weight L is large enough, even if the variables dS and dQ deviate alittle from Eq.(9), the variation of the impurity concentration C isvery small.

An example which satisfies the special equation (10) is now explained.

In this example the relative pulling velocity of the single crystal (8)is 5 mm/H, the diameter of the single crystal (8) is 50 mm, and thediameter of the undoped crystal (9) to be replenished is 15 mm. Thenfrom Eq.(10) the most pertinent relative velocity of the undoped crystaldipping into the melt should be

    (1-k)×55.6 (mm/H)

In the example shown in FIG. 1 the undoped crystal (9) is a pillar. Andit is enclosed by the encapsulant-supporting-cylinder (12). Thesupplying device comprises the supplying shaft (10), the cylinder (12)and the supporting device (not shown in FIG. 1) which rotates andsuspends the supplying shaft (10). In the disposition the cylinder (12)dips into the melt (5) at the peripheral region of the crucible (4).

This disposition of the cylinder breaks a rotational-symmetry of themelt.

The crucible (4), the susceptor (3), the lower shaft (2) and the melt(5) rotate in the crystal growth. The non-symmetric disposition of thecylinder may make a perturbation on the liquid-solid interface (15). Theperturbation may hinder the cylindrical growth of a crystal.

FIG. 2 shows another embodiment of the invention. This embodiment isimmune from the perturbation of the non-symmetric disposition of thesupplying device.

In this embodiment a non-doped crystal (9) to be replenished is shapedin a large cylinder whose diameter is a little smaller than that of thecrucible (4). And the cylinder of the non-doped crystal (9) is enclosedby a double cylinder (12'). In a gap between the double cylinder (12')and the cylindrical non-doped crystal (9) a liquid encapsulant (16) isfilled. Then the double cylinder (12') is called anencapsulant-supporting-double-cylinder.

The disposition and the shape of theencapsulant-supporting-double-cylinder (12') has a perfect rotationalsymmetry. The existence of the cylinder (12') does not disturb therotation of the melt (5). No perturbation would occur on theliquid-solid interface (15).

In this case an encapsulant-heater (14) is a double coiled heaterinstalled at a pertinent height of the double cylinder (12'). Analternative of an encapsulant-heater (14) is an assembly of severalsmall heaters which are disposed with several fold symmetry. And two orthree identical supporting shafts (10) should be installed.

Now we consider the height of the liquid encapsulant (16) for coveringthe undoped crystal (9).

What is important is a height H which is defined as a distance from thesurface of the lower liquid encapsulant (6) to the surface of the upperliquid encapsulant (16).

"h" denotes a distance from the liquid-solid interface (15) to thebottom end of the encapsulant-supporting-cylinder (12) or doublecylinder (12').

"h₁ " denotes a distance from the normal liquid-solid interface (15) tothe suppressed liquid-solid interface (17) in theencapsulant-supporting-cylinder (12) or double cylinder (12').

"ρ_(0") is a density of the compound melt (5). "ρ_(1") is a density ofthe liquid encapsulant (6) or (16). The height H is a function of theinterface difference h₁. Simple calculations lead to

    H=(ρ.sub.0 /ρ.sub.1 -1)h.sub.1                     (13)

It is desirable that H is higher, because the greater part of theundoped crystal (9) is covered with the liquid encapsulant (16).

The height H is in proportion to h₁ from Eq.(13). The suppressedliquid-solid interface (17) is kept by theencapsulant-supporting-cylinder (12) or double cylinder (12'). Thus themaximum of the variable h₁ is equal to h. Then the maximum of the heightH is obtained from Eq.(13) by replacing h₁ by h.

Accordingly it is important that the bottom end of theencapsulant-supporting-cylinder (12) or double cylinder (12') is dippeddeep into the compound melt (5) and much encapsulant material is filledin the cylinder (12) or double cylinder (12').

In the case of the crystal growth of GaAs the density ρ₀ of the melt is5.7 g/cm³ and the density ρ₁ of liquid B₂ O₃ is 1.6 g/cm³. The ratio ofH to h₁ is about 2.6.

Advantages of this invention are now explained.

(1) The impurity concentration of a single crystal grown by theinvention is uniform from seed end to tail end.

This is because the impurity concentration of the melt is kept to beconstant by replenishing an undoped poly-crystal or single crystal intothe melt.

(2) The separating of impurity near the tail end of a crystal does notoccur, because the impurity concentration is uniform in the growncrystal. Therefore whole of a crystal is available for making variouselectronic devices. Waste portion of the crystal is very little.

(3) There happens no deviation from stoichiometry of compounds of groupsIII-V or groups II-VI.

Heated portion of an undoped crystal to be replenished is covered with aliquid encapsulant which is pressed by N₂ gas or inert gas with a highpressure. Volatile elements of group V do not escape from the undopedcrystal.

This invention has a wide scope of applicability. This is fullyapplicable for all kinds of crystal growth by an LEC method. Theexamples of the matrix crystals are GaAs, GaP, InP, InAs, GaSb, PbTe,PbSe, etc.

Impurities doped into the matrix compound are one or more than oneelements among S, B, Te, Sn, Sb, In, Si, Cr, Fe, As, and so on whichhave a distribution coefficient less than 1 in the matrix compound melt.

What we claim is:
 1. An LEC method for growing a single crystal ofcompound semiconductors comprising the steps of:melting a liquidencapsulant material and a compound semiconductor material doped with animpurity with a distribution coefficient of less than 1 to form acompound melt covered by molten liquid encapsulant, dipping a seedcrystal into the compound melt, growing a single crystal from thecompound melt by pulling up and rotating the seed crystal; whilesupplying a solid undoped polycrystal or single crystal of the compoundsemiconductor material covered with a liquid encapsulant to the compoundmelt at a rate to maintain the impurity concentration in the compoundmelt at a substantially constant value.
 2. An LEC Method as claimed inclaim 1, wherein a weight (dQ/dt) of the undoped crystal supplied perunit time and a weight (dS/dt) of the single crystal grown per unit timesatisfy the equation:

    dQ/dt=(1-k)dS/dt

where k is a distribution coefficient of the impurity in the compoundmelt.
 3. An LEC method as claimed in claim 1, wherein the compoundsemiconductor material is one of the compounds of groups III-V.
 4. AnLEC method as claimed in claim 1 wherein the compound semiconductormaterial is one of the compounds of groups II-VI.
 5. An LEC method asclaimed in claim 3, wherein the compound semiconductor material is GaAsand the impurity whose concentration should be kept constant is selectedfrom the group consisting of S, Te, Sn, Si, Cr, Fe, In, Sb, and B.
 6. AnLEC method as claimed in claim 3, wherein the compound semiconductormaterial is InP and the impurity whose concentration should be keptconstant is selected from the group consisting of Sn, Te, S, As, and Sb.7. An LEC method as claimed in claim 1, wherein the supplying stepcomprises the step of supplying a pillared crystal enclosed by anencapsulant-supporting-cylinder,a relative ascending velocity U* of thesingle crystal and relative descending velocity V* of the undopedcrystal satisfy the equation:

    F.sup.2 V*=(1-k)E.sup.2 U*

where F is a radius of the undoped crystal and E is a radius of thegrown crystal.
 8. An LEC method as claimed in claim 1, wherein anascending velocity U of the single crystal, an ascending velocity W ofthe crucible and a descending velocity V of the undoped single crystalsatisfy the relation: ##EQU2## where A is an area of a liquid-solidinterface, B is a sectional area of the grown single crystal, and C is asectional area of the undoped crystal to be replenished.
 9. An LECmethod for growing a single crystal of compound semiconductorscomprising the steps of:melting a liquid encapsulant material and acompound semiconductor material doped with an impurity with adistribution coefficient of less than 1 to form a compound melt coveredby molten liquid encapsulant, dipping a bottom end of a solid undopedpolycrystal or single crystal of the compound semiconductor materialinto the compound melt, the solid undoped polycrystal or single crystalbeing supported by at least one supplying shaft and enclosed by anencapsulant-supporting cylinder with a liquid encapsulant materialtherein, melting the liquid encapsulant material in theencapsulant-supporting cylinder by an encapsulant heater surrounding theencapsulant-supporting cylinder, dipping a seed crystal into thecompound melt covered by the molten liquid encapsulant, growing a singlecrystal from the compound melt by pulling up and rotating the seedcrystal; while supplying the solid undoped polycrystal or single crystalof the compound semiconductor material covered with the liquidencapsulant in the encapsulant-supporting cylinder to the compound meltby lowering the supplying shaft at a rate to maintain the impurityconcentration in the compound melt at a substantially constant value.